Epoetin alfa can increase hemoglobin levels in chronic renal failure patients (patients with persistent kidney dysfunction) resulting in minimal transfusion requirements and improved kidney function capacity. This study is a randomized (patients randomly divided into groups), multicenter, open-label (study drug is known to the patients) clinical trial to assess the effect of normalization of hemoglobin (defined as a hemoglobin level of 13-14 g/dL in women and 14-15 g/dL in men) on the rate of progression of chronic renal failure (persistent kidney dysfunction). The study duration is 40 months. The study is in two phases (Phase A = stabilization, Phase B = maintenance) with two patient groups (Group 1, Group 2) per phase. In Phase A (lasting 4 months) for patients in Group 1, hemoglobin is progressively increased to a target level. Phase A can be extended up to 6 months for Group 1 patients in whom the target hemoglobin (13-14 g/dL in women, 14-15 g/dL in men) is not reached. Patients in Group 2, hemoglobin is progressively increased up to 12 g/dL with epoetin alfa if it drops below 11 g/dL. For all patients in Phase A, Iron and vitamin deficiencies will also be corrected, and factors known to affect progression of renal failure (kidney dysfunction) will be optimized. In Phase B (lasting 36 months), effectiveness of anemia correction by epoetin alfa will be compared against non-correction (continued anemia) with regard to changes in kidney function. During this phase, patients will be maintained at the higher (Group 1) or lower (Group 2) target hemoglobin level. Safety data (including cardiovascular events, seizures, and hypertension) will be collected and monitored throughout the study. The hypothesis of the study is that correction of anemia may slow down kidney deterioration and progression of kidney failure to end-stage kidney disease that is caused by anemia-induced hypoxia, a state of oxygen deficiency in the kidney. Another hypothesis of the study is that genetic mutations (changes in the genes) may play a role in the progression of chronic renal failure. For those patients wishing to participate in this aspect of the study, blood samples will be collected for genomic DNA analysis and the results will be compiled to determine which genes are generally associated in the study population with kidney deterioration. Patients will receive epoetin alfa injections (25 to 100 IU/kg) under the skin 1 time per week. Dosage may be increased by 25 IU/kg increments to reach or maintain target hemoglobin, then dose maintained for study duration, as long as hemoglobin stays within range.